On the boundedness of the periodic Hilbert transform on generalized periodic Morrey spaces

Sheraly Baituyakov, Zhuldyz Baituyakova, Meruert Ilyasova

2016

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DOI 10.1063/1.4959745
Data confidence 70 medium
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Abstract

The Hilbert transform is one of the most important operators in the field of signal theory. Mainly, the importance of the transform is due to its property to extend real functions into analytic functions. This property certainly induces a vast number of applications, especially in signal theory, and obviously the Hilbert transform is not merely of interest for mathematicians.In this paper we prove the boundedness of periodic Hilbert transform on generalized periodic Morrey spaces. As a consequence we able to give uniform estimates of the operator norms of the partial sums on generalized periodic Morrey spaces.